Mathematical competitions play a key role in the promotion of extracurricular education, as they stimulate interest in mathematics, reveal hidden talents, and encourage in-depth problem-solving. The Kangaroo of Mathematics, a globally established multiple-choice competition with millions of participants, serves as an ideal subject for examining the interplay between traditional problem-solving and digital integration. This research builds on the work of Geretschläger and Donner (2022) to discuss how criteria for task selection must evolve alongside digitalization. The aim is to investigate whether moving a competition from paper to screen is a neutral technical change or if it alters the measured competencies. Central to this discussion is the balance between the opportunities for inclusion—such as accessible formats for students with disabilities —and the risks of the "digital divide" and environmental hidden costs of EdTech. This study specifically asks whether the mode of participation is associated with systematic performance differences and how these compare to annual learning progress.

The analysis is based on a longitudinal dataset of the Austrian national cohort from 2023 to 2025 (n = 30,000), where a digital version (n = 3,000) was introduced as a direct, task-by-task replica of the paper-based format. To account for the complex dependencies within this cohort, a linear mixed model (LMM) was specified. The relative score served as the dependent variable, allowing for comparisons across grade levels with varying task counts. The model included the test medium (online vs. offline), the year, and the specific competition category as fixed effects, while utilizing a random effect for individual student IDs. This statistical approach "filters out" the individual ability levels of students observed over multiple years, ensuring that the measured effect is attributable to the medium itself.

The quantitative results reveal that participants in digital formats systematically achieved lower scores than those in analogue environments. After controlling for individual talent, test year, and specific task difficulty, a stable "online gap" persists. While digitalization is often seen as a tool for progress, these findings suggest a consistent disadvantage for students working on screens. Interestingly, this gap is non-trivial when compared to the natural annual learning progress observed within the same test categories. In contrast to digital designs explicitly intended for exploration—such as the Bulgarian "Theme of the month" where tasks utilize interactive GeoGebra applets —the direct transfer of paper-pencil tasks appears to introduce structural friction. These results support the hypothesis that the medium alters problem-solving practices, potentially due to the inability to sketch directly on the task or the increased cognitive load of managing on-screen information.

The educational significance of this research lies in the move from experience-based design to evidence-based transformation. The results suggest that transferring mathematics competitions to digital environments without explicitly adapting the task and test design can lead to structural disadvantages. Digitalization should not be viewed as an end in itself, but as a deliberate integration that requires specific pedagogical considerations. These findings provide organizers and schools with a foundation for developing digital assessments that maintain equity and validity. Ultimately, the goal is to ensure that the transition to digital formats supports the core objective of mathematical competitions: providing a joyful, insightful, and fair experience for all students.

Team-based academic competitions are increasingly used as a complement to traditional individual formats in secondary education. This matters because participation is no longer only an individual cognitive achievement, but also a social process under time pressure. At the international level, this trend is visible in the Náboj ecosystem. The official mathematics page lists 15 participating countries for March 2026, while the current physics page reports participation across 8 countries in the latest cycle. At the same time, regional formats such as e.g., m3 in Austria and MatheMixDoppel in Styria create additional pathways into STEM competition culture. Across these formats, team sizes differ, allowing us to investigate whether collaboration structures influence attractiveness for participants. Building on interest research, we distinguish between interest in the domain and interest in the activity of collaborative problem solving. The study examines the social dimension of competition success and asks how team size relates to enjoyment of teamwork, how enjoyment relates to perceived popularity, and which student-reported mechanisms explain these relations.

We conducted an explorative mixed-method study in Styria, Austria. Data were gathered through questionnaires in team competitions hosted at University of Graz: MatheMixDoppel, m3 and Nábo. In total, 445 questionnaires were collected. The instrument included two metric items and eight open-ended items. The metric items captured enjoyment of teamwork and perceived attractiveness of the format. The open items were mainly feedback to different aspects of the competition and tasks. Open responses were analyzed with structuring qualitative content analysis according to Mayring, starting with deductive categories.

The findings show a consistent social mechanism. Team size is meaningfully associated with reported enjoyment of teamwork, and enjoyment of teamwork is strongly associated with perceived popularity of the competition format. Social experience is therefore not a peripheral outcome of participation, but a central driver of format success. The qualitative material explains this pattern in detail. Students more often mentioned teamwork as motivating and fun when the group size was larger, a logistic regression shows a significant dependency on group size.

Educationally, the study offers actionable implications for organizers, teachers, and policy actors. Team size should be treated as a pedagogical design variable, not merely a logistical setting. Task and rule design should intentionally scaffold collaboration through multiple entry points, complementary responsibilities, and transparent submission routines. Short pre-competition preparation on communication and coordination norms can improve inclusion and reduce avoidable friction. This is especially relevant for schools seeking low-threshold entry points into STEM participation. Overall, the results suggest that high cognitive demand and broad participation are not competing goals. When social design is deliberate, team competitions can be both academically rigorous and motivationally inclusive, and can strengthen sustained engagement in mathematics and physics for diverse groups of secondary students.

Mathematical modelling is a well-established part of school mathematics, yet its implementation remains contested. In many classrooms, modelling appears as short, strongly guided tasks, whereas project formats offer more time for iteration, collaboration, and reflection on limitations. This study addresses that tension through the International Mathematical Modeling Challenge (IM²C), a global team competition in which students work intensively on one socially relevant modelling problem over several days. The 2024 challenge, focused on pet ownership, required teams to define “pet,” develop criteria for “pet-readiness,” and model future developments across different cultural contexts. Against this background, we investigate how IM²C functions as a location-independent format for realistic/applied modelling, which strengths and recurring difficulties emerge in submissions from the German-speaking context, and which pedagogical conditions are needed if participation is to be meaningfully connected to regular mathematics teaching rather than treated as an isolated extracurricular event.

The study uses a qualitative comparative document analysis. The empirical corpus consists of IM²C 2024 submissions from the German-speaking context and two awarded papers that serve as benchmark cases of high-quality modelling practice. Our analytic procedure combines theory-driven and inductive coding. The theory-driven dimensions include problem framing and operationalization, assumptions and simplifications, data selection and data-quality handling, model construction and mathematical reasoning, validation and uncertainty treatment, and interpretation and communication of recommendations. Inductive refinement was used to capture recurring patterns not fully covered by the initial framework, especially in places where teams negotiated value-laden terms. Analysis proceeded in two steps: first, within-case reconstruction of each team’s modelling pathway and key decision points; second, cross-case synthesis to identify stable patterns, contrasts, and quality markers. Interpretive rigour was strengthened through analytic memos, iterative recoding, and contrastive comparison with the awarded benchmark reports.

The findings show that IM²C can elicit modelling activity far beyond routine textbook problem solving. Many teams engaged deeply with framing, and the operational definition of “pet” together with the construction of “pet-readiness” indicators became the epistemic pivot of the entire modelling process. Reports that made these choices explicit generally produced more coherent models and more defensible conclusions. Across cases, three strengths were recurrent: creative development of indicators and composite criteria, interdisciplinary reasoning that linked mathematical analysis to social and cultural considerations, and comparatively strong communication for non-specialist audiences. At the same time, three bottlenecks appeared repeatedly: limited depth of validation, weak treatment of uncertainty and sensitivity, and overconfident projections from sparse or heterogeneous data. A further issue concerned the interplay of normative and empirical reasoning: in several reports, value-based thresholds were presented as if they were purely data-driven, blurring an important boundary between descriptive modelling and normative judgment. Comparison with the two awarded reports suggests that excellence depended less on advanced formal mathematics alone and more on methodological coherence: transparent assumptions, disciplined simplification, explicit handling of limitations, and reflective interpretation of results. These findings also highlight an implementation tension: while location-independence broadens access, participation quality is still shaped by unequal mentoring intensity, data-literacy support, and project management structures.

Educationally, the study contributes to an under-researched but influential learning environment: competition-based, project-extended modelling in STEM education. The results indicate that IM²C can function as a bridge between school mathematics and authentic societal inquiry while promoting collaboration, argumentation, and responsible quantitative judgment. For practice, the analysis supports a three-phase integration into regular instruction: targeted preparation before participation (especially on assumptions, validation, and uncertainty), milestone-based mentoring during team work, and structured post-project reflection that reconnects competition experiences to curricular learning goals. For teacher education, the findings underline that modelling quality should not be assessed only by technical correctness or final numerical output; equal weight should be given to transparency of assumptions, quality of validation, and critical interpretation of limits. In this sense, IM²C is not merely a high-achievement contest, but a didactical resource for developing mathematically informed judgment in complex real-world contexts.